# A Different View of Sigma-Delta Modulators Under the Lens of Pulse Frequency Modulation

arXiv: https://arxiv.org/abs/2311.06983 · HTML: https://mlsanity.com/paper/2311.06983/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2023.

## Built on by (most cited first, 1 of 1)

- [Analytical Derivation of Quantization Error in Threshold Level Quantizers Using Bipolar PFM](https://mlsanity.com/paper/2602.17471/) (2026)

## Abstract (arXiv)

The fact that VCO-ADCs produce noise-shaped quantization noise suggests that a link between frequency modulation and Sigma-Delta modulation should exist. The connection between a VCO-ADC and a first-order Sigma-Delta modulator has been already explained using Pulse Frequency Modulation. In this paper, we attempt to extend the theory based on Pulse Frequency Modulation to a generic Sigma-Delta modulator. We show that this link between Sigma-Delta modulation and Pulse Frequency Modulation relies in a sampling invariance property that defines the equivalence between both entities. This novel point of view, allows to go beyond the white quantization noise model of a Sigma-Delta modulator, revealing the origin of some nonlinear phenomena. We first predict spurious tones which cannot be explained by circuit non linearity. Multi-bit and single bit modulators are shown to belong to a same generic class of systems. Finally, quantizer overload is analyzed using our model. The results are applied to Continuous-Time Sigma-Delta modulators of orders one, two and three and then extended to a generic case.